>> >  POV-Ray, however, handles mathematical primitives (such as boxes and
>> > planes) and their CSG. Rounding their corners is a problem which is
>> > several orders of magnitude harder.
>
>> But not impossible, look at any CAD software that manages it with
>> mathematically defined CSG.
>
>  CAD software always tesselate their geometry before rendering. They do 
> not
> render untesselated mathematical surfaces.

That's only to render quickly though, internally all surfaces are stored as 
mathematical descriptions.  In theory you could write a raytracer to render 
these surface descriptions directly with no tesselation.  In fact, if you 
create a shape with rounded edges in a CAD program, you can export it to a 
common interchange format (STEP) which is plain text.  In that you will see 
that the solid is completely defined by mathematical curves and surfaces, no 
tesselation.

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